A discrete replacement model for a two-unit parallel system subject to failure rate interaction

In this paper, a repairable two-unit parallel system with failure rate interaction between units is studied. Failure rate interaction between units is described as follows. Unit-1 failure whenever occurs can increase the failure rate of unit-2 of some amount, while unit-2 failure can induce unit-1 into simultaneous failure. We consider a discrete replacement policy N based on the number of unit-1 failure. The system is replaced at the instant of the N-th failure of unit-1 or on simultaneous failure of the system. Our problem is to determine an optimal replacement policy N ^* such that the expected cost rate per unit time is minimized. The explicit expression of the expected cost rate per unit time is derived by introducing relative costs and the corresponding optimal number N* is also verified finite and unique under some specific conditions.     

Periodical Replacement Model for a Multi-Unit System Subject to Failure Rate Interaction

A periodical replacement model for a multi-unit system subject to failure rate interaction between units is presented. In a N-unit system, one is dominant unit and the others are secondary units. When a secondary unit fails, it increases the failure rate of the dominant unit by some amount, while the failure of dominant unit make the system into total failure. Without failure rate interaction, the failure rates of all units also increase with age. All single failures of secondary units are assumed to be corrected by minimal repairs. The system is replaced at age T, or on total failure, whichever occurs first. The aim of this paper is to derive the expected cost rate per unit time as a criterion of optimality and to seek the optimal period T ^* to minimize that cost rate.